Hardy-Weinberg's Principle

The Hardy-Weinberg principle, also known as the Hardy-Weinberg equilibrium law, states that at equilibrium, both the gene (allele) frequency and the genotypic frequency of a population remain constant from one generation to the next. This equilibrium, however, holds only under specific conditions: the population must be diploid, sexually reproducing, large, and freely interbreeding, with mating occurring at random and with no selection or other disturbing factor acting to change the allele frequency.

Consider, for example, a single genetic locus with just two alleles, A and a, whose frequencies in the population are p and q respectively. Because these are the only two alleles present at this locus, their frequencies must together add up to one: p + q = 1. The corresponding genotypic frequencies can then be found by squaring this relationship, (p + q)² = 1, which expands (as a standard binomial expansion) to p² + 2pq + q² = 1 — where p² represents the frequency of the homozygous dominant genotype AA, q² represents the frequency of the homozygous recessive genotype aa, and 2pq represents the frequency of the heterozygous genotype Aa. This can be explained by a Punnett square, as follows: